$\dfrac{ -4v - 9w }{ 8 } = \dfrac{ -5v - 5x }{ 4 }$ Solve for $v$.
Multiply both sides by the left denominator. $\dfrac{ -4v - 9w }{ {8} } = \dfrac{ -5v - 5x }{ 4 }$ ${8} \cdot \dfrac{ -4v - 9w }{ {8} } = {8} \cdot \dfrac{ -5v - 5x }{ 4 }$ $-4v - 9w = {8} \cdot \dfrac { -5v - 5x }{ 4 }$ Reduce the right side. $-4v - 9w = {8} \cdot \dfrac{ -5v - 5x }{ {4} }$ $-4v - 9w = {2} \cdot \left( -5v - 5x \right)$ Distribute the right side $-4v - 9w = {2} \cdot \left( -{5v} - {5x} \right)$ $-4v - 9w = -{10}v - {10}x$ Combine $v$ terms on the left. $-{4v} - 9w = -{10v} - 10x$ ${6v} - 9w = -10x$ Move the $w$ term to the right. $6v - {9w} = -10x$ $6v = -10x + {9w}$ Isolate $v$ by dividing both sides by its coefficient. ${6}v = -10x + 9w$ $v = \dfrac{ -10x + 9w }{ {6} }$